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Metamath Proof Explorer

Theorem sdomnen

Description: Strict dominance implies non-equinumerosity. (Contributed by NM, 10-Jun-1998)

Ref Expression
Assertion sdomnen 
|- ( A ~< B -> -. A ~~ B )

Proof

Step Hyp Ref Expression
1 brsdom 
 |-  ( A ~< B <-> ( A ~<_ B /\ -. A ~~ B ) )
2 1 simprbi 
 |-  ( A ~< B -> -. A ~~ B )